Simultaneous Higher-order Relation Prediction via Collective Incidence Matrix Embedding
Simultaneous Higher-order Relation Prediction via Collective Incidence Matrix Embedding
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DOI：
10.1527/tjsai.30.459
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发表时间：
2015
影响因子：
--
通讯作者：
Nozomi Nori;Danushka Bollegala;H. Kashima
中科院分区：
文献类型：
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作者：
Nozomi Nori;Danushka Bollegala;H. Kashima
我们提出了一种预测方法，高阶关系数据从多个来源。高阶关系的高维属性会导致与稀疏观测相关的问题。为了科普这个问题，我们提出了一种方法来集成高阶关系数据从多个来源。我们的目标任务是同时分解高阶多关系数据，这对应于同时分解多个张量。然而，我们将每个张量转化为相应的超图的关联矩阵，并应用非线性降维技术，从而保证全局最优解的广义特征值问题。我们还扩展了我们的方法，将对象的属性信息，以提高预测看不见/未观察到的对象。据我们所知，这是第一个报告的方法，可以预测（1）高阶关系（2）与多关系数据（3）与对象属性信息和（4）保证全局最优解。使用来自社交网络服务的真实数据集，我们证明了我们提出的方法比高阶单/多关系数据（包括非负多重张量因子分解）的最新方法对数据稀疏性更鲁棒。
We propose a prediction method for higher-order relational data from multiple sources. The high-dimensional property of higher-order relations causes problems associated with sparse observations. To cope with this problem, we propose a method to integrate higher-order relational data from multiple sources. Our target task is the simultaneous decomposition of higher-order, multi-relational data, which corresponds to the simultaneous decomposition of multiple tensors. However, we transform each tensor into an incidence matrix for the corresponding hypergraph and apply a nonlinear dimensionality reduction technique that results in a generalized eigenvalue problem guaranteeing global optimal solutions. We also extend our method to incorporate objects’ attribute information to improve prediction for unseen/unobserved objects. To the best of our knowledge, this is the first reported method that can make predictions for (1) higher-order relations (2) with multi-relational data (3) with object attribute information and which (4) guarantees global optimal solutions. Using real-world datasets from social web services, we demonstrate that our proposed method is more robust against data sparsity than state-of-the-art methods for higher-order, single/multi-relational data including nonnegative multiple tensor factorization.